document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=562910>Question 562910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train running from A to B meets with an accident 50 miles from A, after which it travels 3/5 of its original velocity and arrives 3 hours late at B; if the accident has occurred 50 miles further on, it would have been 2 hours late. Find the distance from A to B and the original velocity of the train? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #364939 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=364939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A train running from A to B meets with an accident 50 miles from A, after which it travels 3/5 of its original velocity and arrives 3 hours late at B;<BR>\n" );
document.write( " if the accident has occurred 50 miles further on, it would have been 2 hours late. <BR>\n" );
document.write( "Find the distance from A to B and the original velocity of the train?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = normal speed of the train<BR>\n" );
document.write( "then<BR>\n" );
document.write( ".6s = speed after accident<BR>\n" );
document.write( ":<BR>\n" );
document.write( "d = distance from A to B<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = normal travel time of the train from A to B<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 3 = travel time after 50 mi accident<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2 = travel time after 100 mi accident<BR>\n" );
document.write( ":<BR>\n" );
document.write( "50 mi accident travel time equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2Fs ALIGN=MIDDLE  ALT=\"50%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28d-50%29%29%2F%28.6s%29 ALIGN=MIDDLE  ALT=\"%28%28d-50%29%29%2F%28.6s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 3<BR>\n" );
document.write( "multiply by .6s to clear the denominators, results<BR>\n" );
document.write( ".6(50) + (d-50) = .6d + .6s(3)<BR>\n" );
document.write( "30 + d - 50 = .6d + 1.8s<BR>\n" );
document.write( "d - 20 = .6d + 1.8s<BR>\n" );
document.write( "d - .6d - 1.8s = 20<BR>\n" );
document.write( ".4d - 1.8s = 20<BR>\n" );
document.write( ":<BR>\n" );
document.write( "100 mi accident travel time equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2Fs ALIGN=MIDDLE  ALT=\"100%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28d-100%29%29%2F%28.6s%29 ALIGN=MIDDLE  ALT=\"%28%28d-100%29%29%2F%28.6s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2<BR>\n" );
document.write( "multiply by .6s, results<BR>\n" );
document.write( ".6(100) + (d-100) = .6d + .6s(2)<BR>\n" );
document.write( "60 + d - 100 = .6d + 1.2s<BR>\n" );
document.write( "d - 40 = .6d + 1.2s<BR>\n" );
document.write( "d - .6d - 1.2s = 40<BR>\n" );
document.write( ".4d - 1.2s = 40<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Subtract the 1st equation from the above equaton<BR>\n" );
document.write( ".4d - 1.2s = 40<BR>\n" );
document.write( ".4d - 1.8s = 20<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "+.6s = 20<BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F.6 ALIGN=MIDDLE  ALT=\"20%2F.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 33<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph is the normal train speed<BR>\n" );
document.write( "Find d<BR>\n" );
document.write( ".4d - 1.2(33.33) = 40<BR>\n" );
document.write( ".4d - 40 = 40<BR>\n" );
document.write( ".4d = 40 + 40<BR>\n" );
document.write( ".4d = 80<BR>\n" );
document.write( "d = 80/.4<BR>\n" );
document.write( "d = 200 mi is the distance<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if the that checks out in the 100 mi accident equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F33.33 ALIGN=MIDDLE  ALT=\"100%2F33.33\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28200-100%29%29%2F%28.6%2833.33%29%29 ALIGN=MIDDLE  ALT=\"%28%28200-100%29%29%2F%28.6%2833.33%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F33.33 ALIGN=MIDDLE  ALT=\"200%2F33.33\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 2<BR>\n" );
document.write( "3 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F20 ALIGN=MIDDLE  ALT=\"100%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6 + 2<BR>\n" );
document.write( "3 + 5 = 6 + 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can say: normal speed = 33<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph; distance is 200 mi<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );